{
  "id": "2203.06057",
  "version": "v1",
  "published": "2022-03-11T16:29:51.000Z",
  "updated": "2022-03-11T16:29:51.000Z",
  "title": "Extremes of the stochastic heat equation with additive Lévy noise",
  "authors": [
    "Carsten Chong",
    "Péter Kevei"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We analyze the spatial asymptotic properties of the solution to the stochastic heat equation driven by an additive L\\'evy space-time white noise. For fixed time $t > 0$ and space $x \\in \\mathbb{R}^d$ we determine the exact tail behavior of the solution both for light-tailed and for heavy-tailed L\\'evy jump measures. Based on these asymptotics we determine for any fixed time $t> 0$ the almost-sure growth rate of the solution as $|x| \\to \\infty$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-03-11T16:29:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60H15",
      "60F15",
      "60G70",
      "60G17",
      "60G51"
    ],
    "keywords": [
      "additive lévy noise",
      "additive levy space-time white noise",
      "stochastic heat equation driven",
      "spatial asymptotic properties",
      "almost-sure growth rate"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}